e: 4. Find the distance from the point (0, 0) to the line with the equation y-7x-8

Q: (d). Consider the line y = ax , where a is a positive constant. What is the shortest distance…

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Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

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Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

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Q: For what values of a and b is the line 5x + y = b tangent to the parabola y = ax? when x = 4?

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And…

Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Consider the relation between r and y defined by the equation r4/3+y4/3 = 10. Find the r-intercept…

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Find the coordinates of the point in the curve y = 12x - 2y + 23 that is nearest to the point…

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Q: (d) Find the points on the curve x'y = 60 nearest the origin.

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Q: nd the midpoint M of the line segment joining the points C = (0, 8) and D = (-8, 4). M = 0D Dlo

A: Given:- points C(0,8) and D(-8,4) To find:- mid point of line joining points C and D

Q: Find the exact length of the curve. x = e - 9t, y = = 12e2, 0 sts 4

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Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: Q4/ Find the angle between the curves x² = y & y² = x

A: The curves intersect at (1,1).  Now calculate slope at (1,1):  ddxx21,1=ddxy1,12x1,1=dydx1,1m1=2…

Q: Find the equation of the set of points which are equidistant from (3,10) and the x-axis. OA 1 y=…

A: Given set is equidistance from (3,10) and the x-axis

Q: Find the point (a, b) on the graph of y = e^x where the value ab is as small as possible.

A: Solution:Given y=exTo find(a,b)  where ab is as small as possible.

Q: For what values of a and b is the line 2x +y= b tangent to the curve y = ax' when x = -5? a = b =…

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Q: H.W.I Find the distance from the pointC2,,3) and the line

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Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

Q: Q3/ Find the angle between two curves: 3 x2 , y = x² y = 2

A: Please see the answer in step 2

Q: Q5/ Find the equation of the circle tangent to the lines y=2, x-3 and y = x+2.

A: Explained below

Q: The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find th…

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Q: Q2/ Find the equation of the circle tangent to the lines, y -2x+3, y = - 2x+7, y=+ and y =+

A: In the above question we have to find the equation of the circle at the tangents -  y= -2x+3 ; y =…

Q: The line y = kr + 4, where k is a constant, is graphed in the xy-plane. If the line contains the…

A: Given line is: y = kx + 4 ................... (1) The line contains the point (c, d). Then (c, d)…

Q: 4. The tangent of the acute angle between the lines y= 4x- 3 and y=x-5 is А. 5 В. C. 3 D. 5

A:

Q: 2. Find x, y, and z. 10 5. 3. To estimate the height of a radio to until his line of sight to the…

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Q: Q2/ Find the equation of the circle tangent to the lines, y =-2x+3, y = - 2x+7, y-+늘and y- +글 %3D…

A: The lines given by y=-2x+3 and y=-2x+7 will be parallel to each other as they have the same slope m.…

Q: 2(m+1)x2 + 4mxy + (m+2)y2 + 2x - 2y = 0 Investigate which curve the equation shows according to the…

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Q: B 1+ 1 D А 5. Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is…

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Q: D. Find the equations of tangent to circle x +y 2 -16x -12y +87 = 0 at y = 4 (Write the equation of…

A: The equation of the circle is  x2+y2-16x-12y+87=0

Q: Find the point on the graph y=Vx+1 that is closest to the point (2, 1).

A:

Q: on the line ye -2x +8 that 1-) Find the point IS Close't to the onigin.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: Find the coordinates of the point in the curve y = 12x – 2y + 23 that is nearest to the point P(10,…

A: Given curve: y2=12x-2y+23 The point is  P10,4 To find: The coordinates of the point on the curve…

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 4? a = b…

A:

Q: At what points will the line y =x intersect the unit circle x2 +y2 =1 ?

A: We have to find the points where line y=x is intersecting the unit circle: x2+y2=1 To find the…

Q: Luna calculates d, and also the distance d, from the point E to the line through D and F and notices…

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Q: Given the curve y= x^3 - 4x + 1 . Find the equation of the line perpendicular to that curve at…

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Q: Q2) A- Find the distance between the line (y = x + 3 ) and center of circle (x²+y²–2x=0).

A: Topic : Coordinate Geometry  Answer  question no 2 :- sqrt(8) As per our guidelines,  at a time only…

Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

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Q: The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find the…

A: The solution for the above solution is as shown below.

Q: Find the distance between the parallel lines.

A: Here x1 = 1; x2 = 0; y1 = 0; y2 = 1; z1 = -1; z2 = 1

Q: Q1/ Find the equation of the circle tangent at least to three lines (y= 1, y= 5, x= 2 and x=7). 40%

A:

Q: For what values of aa and bb is the line −4x+y=b-4x+y=b tangent to the curve y=ax2y=ax2 when…

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Q: S. 3 z dz where C is straight line segment from i to -2 - 3i

A: We put z=x+iy And dz=dx+idy

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.